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A square is the 2-dimensional hypercube. It has the schläfli symbol ${\displaystyle \{4\}}$, as it is a four-sided polygon. Other names of square are called tetragon or tetrasquaron (Using Googleaarex's polytope naming system).

Squares are one of the three regular polygons that tile the plane. The others are the equilateral triangle and regular hexagon. A circle area divided by the square area is ${\displaystyle \frac{\pi}{2}}$ in a very special case.

### Sections

The square can be thought of as infinitely mine line segments stacked on each other in the y direction. As such, when viewed from a side, the sections are identical lines. It is composed of two pairs of parallel line segments.

When viewed from a vertex, the point will expand into a line of length ${\displaystyle \sqrt{2}}$ before turning back to a point.

A square's vertices can be thought of as the combination of all ways you can arrange zero and one on a 2d grid.

### Hypervolumes

• vertex count = ${\displaystyle 4}$
• edge length = ${\displaystyle 4l}$
• area = ${\displaystyle l^2}$

### Subfacets

Zeroth First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth
Simplex Point Line Triangle Tetrahedron Pentachoron Hexateron Heptapeton Octaexon Enneazetton Decayotton Hendecaxennon
Hypercube Point Line Square Cube Tesseract Penteract Hexeract Hepteract Octeract Enneract Dekeract